value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Linear equations in one variable, three prices are to be distributed in a q...

three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of

Pemdas, what is the answer using pemdas (32 divided into 4)+3

what is the answer using pemdas (32 divided into 4)+3

Inverse functions, We have seen that if y is a function of x, then fo...

We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f

Sketch the graph of h (t ) = 1 - 5e 1/(t/2), Sketch the graph of h (t ) = ...

Sketch the graph of h (t ) = 1 - 5e  1/(t/2) Solution : Let's primary get a table of values for this function. Following is the sketch. The major point behin

Curve tracing, How we calculate region for curve tracing

How we calculate region for curve tracing

Numerical integration - simpson rule, (1)Derive, algebraically, the 2nd ord...

(1)Derive, algebraically, the 2nd order (Simpson's Rule) integration formula using 3 equally spaced sample points, f 0 ,f 1 ,f 2 with an increment of h. (2) Using software such

Multiplication properties, write a definition for associative property of m...

write a definition for associative property of multiplication in your own words and explain how you use it to compute 4*25*27 mentally

Set theory, how to prove Decidability Theorem of Logic

how to prove Decidability Theorem of Logic

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd